Estimation of the Percentage of Aid Received from the Food Bank Using a Stratified Sampling

The interval estimate of the percentage of food received from the Food Bank with reference to household necessity is the main purpose of this article. A group of families having difficulty in purchasing enough food and thus receiving it from a charitable organization near Milan was considered. The group of families was divided into two groups depending on whether the householder was Italian or a foreigner. For the interval estimate of the ratio in question to be provided, we use the confidence intervals proposed by Galeone (2007) and Galeone and Pollastri (2012) but, in order to consider that the sample is stratified, it is necessary to introduce new methodologies. In fact, if a stratified sample is used, the properties of the estimator can be improved with respect to the estimator obtained from a simple random sample. In order to take into account the uncertainty of the estimate due to sampling, this paper proposes a new technique for the construction of confidence intervals of the indicator under examination based on the distribution of the ratio of two correlated Normal random variables when the sample is stratified. Using simulations, the confidence intervals for the ratio were compared when using the simple random sample with the confidence intervals based on a stratified sample. As a result, by using the stratified sample, the confidence intervals for the ratio can be improved because the width results reduced. Therefore, a combined ratio estimator was used in order to evaluate whether the help provided to the families satisfies their needs.